A new perspective for assessing hydro-meteorological drought relationships at large scale based on causality analysis

Correlation analysis is the common method to evaluate the relationship between two variables; however, it may sometimes cause spurious correlations. Specifically, in the field of hydrometeorology, with the impacts of climate change and human activities, correlation analysis is difficult to identify the true relationship between variables, and thus, causality analysis should be adopted instead. This study analyzed the causal relationship between meteorological drought and hydrological drought in different climatic regions of China by using convergent cross mapping (CCM). We improved the identification of CCM convergence by using the coefficient of variation and applied it in the field of large-scale hydrometeorology. The results of correlation analysis were compared, and the applicability of causality analysis was explored. The results revealed that: In Southeast China, the correlation and causality between meteorological drought and hydrological drought were both large. In Northeast China and central Qinghai–Tibet Plateau, the correlation between meteorological drought and hydrological drought was small, but the causality was large. In view of the spurious correlation, introducing causality analysis can better explain the relationship between meteorological drought and hydrological drought, especially in areas with snowmelt runoff. Overall, CCM can provide valuable causal information from common time series in the field of large-scale hydrometeorology and has a wide range of application values. However, causality analysis cannot explain the positive or negative relationship between variables. Therefore, when analyzing the relationship between variables, the advantages of the two methods should be given full play.


Introduction
Drought is one of the most common types of disasters in the world, which usually has the characteristics of a large range of occurrence and a long duration.In the context of global warming, both the frequency and intensity of future drought events will show increasing trends (Wang et al 2021).In general, drought can be divided into four types: meteorological drought, hydrological drought, agricultural drought, and socio-economic drought (Van Loon 2015, Zhou et al 2021a, 2021b).Meteorological drought is usually the primary driver of other types of droughts, and it is also the basis for forecasting other types of droughts (Mishra et al 2010, Liu et al 2016a, Han et al 2021, Bas ¸agaoglu et al 2023, Guo et al 2023).Therefore, it is essential to evaluate the relationships between meteorological drought and other types of droughts.
Many scholars have studied the relationship between meteorological drought and hydrological drought from either linear or nonlinear perspective, or both.Apurv et al (2017) assessed the role of climate characteristics in drought propagation.Xu et al (2019) evaluated the impacts of human activities on the propagation from meteorological drought to hydrological drought in northern China from a linear perspective.Ding et al (2021a) evaluated the relationship between meteorological drought and hydrological drought in China by using the Pearson correlation coefficient (PCC) method.Wu et al (2017) constructed a drought propagation model from meteorological drought to hydrological drought by using nonlinear mathematical function.Fang et al (2020) used mutual information to evaluate the nonlinear relationship between meteorological drought and hydrological drought on the Loess Plateau.Zhou et al (2021b) evaluated the nonlinear relationship between meteorological drought and hydrological drought in the Pearl River Basin by using directed information transfer index.As is known, there is a causal relationship between meteorological drought and hydrological drought in essence.Although temperature anomalies may exacerbate hydrological droughts induced by meteorological droughts (Diffenbaugh et al 2015), the main process is precipitation deficit which may lead to runoff deficit, and this relationship is directional (Shi et al 2022a).However, linear or nonlinear correlation is actually an assessment of how close two time series are to each other, which is not a reasonable way to represent directional causality.In addition, the study of Sugihara et al (2012) has shown that there is spurious correlation in correlation analysis, and correlation is not a sufficient and necessary condition for causality.Therefore, causality analysis is essential for avoiding such possible spurious correlation that may exist in hydrometeorological research.
In recent years, causality analysis methods have been used to explore the causal relationship between variables.Zhang and Wang (2020) used causality analysis to preliminarily propose the mechanism of the causality between and Siberian High and winter surface air temperature in Northeast Asia.Liang et al (2021) used the transfer entropy (TE) to seek predictor(s) for El Nino Modoki to enable it to predict 10 years in advance.Kadir et al (2020) showed that convergent cross mapping (CCM) could be suitable for exploring the drivers of the hydrologic alteration in multivariate time series.For the unsolved problem of the mutual feedback between vegetation and soil moisture, Wei et al (2022) used Granger causality (GC) test to solve the problem of the mutual feedback between vegetation and soil moisture in the Loess Plateau.However, GC and TE are equivalent when variables are distributed in Gaussian distribution (Barnett et al 2009, Shi et al 2022a).In addition, in the field of hydrometeorology, since the relationship between variables may be affected by other factors (e.g.terrain, geology, vegetation, and so on), linear conceptualization (e.g.GC) might be inadequate (Sivakumar 2000(Sivakumar , 2009)).Ombadi et al (2020) evaluated the applications of several causality analysis methods (GC, TE, graph-based algorithms, and CCM) to hydrometeorological systems, and the results showed that CCM was suitable for exploring relationships between variables and was insensitive to changes in sample length.In the field of hydrometeorology, sample lengths are usually large.Therefore, CCM has been selected to evaluate the relationship between meteorological drought and hydrological drought (e.g.Shi et al 2022a).
At present, the convergence of the CCM results is mainly judged by the scatterplot of the CCM results, and there is still no appropriate index to quantitatively evaluate the convergence of the CCM results.Specifically, when the scatterplot of the CCM results is relatively chaotic, such method is difficult to identify the final convergence value.Moreover, in large-scale hydrometeorological research (e.g. the grid data), it is hard to judge the convergence value one by one through the scatterplot of the CCM results for each grid.Due to this limitation, CCM is more suitable for the analysis of a single point (e.g. the station data), and the application of CCM to large-scale hydrometeorological research is somehow difficult.To overcome this shortage, it is essential to improve the identification of the convergence value.
To this end, this study aims to provide a new perspective for assessing hydro-meteorological drought relationships based on an improved causality analysis method.Standardized Precipitation Index (SPI) and Standardized Precipitation Evapotranspiration Index (SPEI) are used to represent meteorological drought, Standardized Runoff Index (SRI) is used to represent hydrological drought, and the CCM is used to evaluate the causal relationship between meteorological drought and hydrological drought in different climatic regions of China.The highlights of this study are: (1) to improve CCM by proposing a method to identify the convergence value; (2) to propose a more physical-rational causality analysis instead of overused even spurious correlation analysis in hydrometeorological research; and (3) to compare the correlation and causality between meteorological drought and hydrological drought in different climatic regions, and examine the applicability of the improved causality analysis method.Overall, the improvement of the CCM convergence identification in this study makes CCM more suitable for large-scale hydrometeorological research, and also provides a new perspective for studying the relationships between different types of droughts based on causality analysis at large scale for the first time.

Study area
China is located in the east of Asia, with a land area of about 9.6 million square kilometers.China's terrain is very diverse.China has a wide variety of landscapes, such as vast plains, valleys, mountains, rivers and so on.The spatial distribution of precipitation and temperature in China is nonuniform, with more precipitation in the east (800-1600 mm) and less precipitation in the west (200-800 mm)

Data
In this study, meteorological data (precipitation, temperature, wind speed, sunshine hour, and relative humidity) during 1961-2018 were obtained from the CN05.1 dataset with the temporal resolution of 1 month and spatial resolution of 0.25 • × 0.25 • .This dataset was constructed on the basis of over 2400 stations in China and it has been extensively applied to climate model evaluation and long-term climatic analysis (Gao et al 2013).In this study, the meteorological data were used to calculate drought indices.Miao and Gou (2022a) reconstructed a long time series, full coverage, and high-quality natural runoff grid data set named CNRD v1.0 (China Natural Runoff Dataset version 1.0), which can provide the daily, monthly, and annual estimated runoff in China from 1961 to 2018 with the spatial resolution of 0.25 • × 0.25 • .

Drought indices
In this study, SPI and SPEI were used to represent meteorological drought, and SRI was used to represent hydrological drought.These three indexes can describe drought characteristics at different time scales and are widely used in the field of hydrometeorology (Fu et al 2018, Zhou et al 2020, Ding et al 2021b).Only 1 month scale drought indices are analyzed in this study because it can comprehensively reflect drought characteristics at the monthly scale.The calculation processes of these three indexes are similar, which can be mainly divided into three steps: (1) to calculate the cumulative deficit (i.e.precipitation and runoff for SPI and SRI, precipitation-evapotranspiration (ET) for SPEI) during a certain period; (2) to estimate the cumulative probability of time series values by fitting the longterm cumulative deficit into a probability distribution; and (3) to convert the cumulative probability to a standard normal distribution.For the specific calculation processes of SPI, SPEI, and SRI, please refer to Yao et al (2020) and Wu et al (2017).

Trend analysis methods
In this study, we used Mann-Kendall trend analysis and Sen's slope method recommended by the World Meteorological Organization to analyze the spatialtemporal variation characteristics of precipitation, runoff, and ET.Mann-Kendall trend analysis method is used to indicate the strength of the trend, and Sen slope method is used to indicate the changing magnitude of the trend.These two methods have been widely used in the field of hydrometeorology (Fu et al 2018, Zhou et al 2020), and the specific calculation processes can be referred to Shi and Wang (2015) and Sen (1968).

Correlation and causality
In this study, PCC and CCM were used to analyze the relationship between meteorological drought and hydrological drought.PCC is used to determine the correlation between two sequences and is widely used in the scientific community (Barker et al 2016, Xu et al 2019, Wei et al 2022, Shi et al 2022b), while CCM is used to evaluate the causality between two sequences.Please refer to the Supplementary Data file for the specific calculation processes of CCM.

Evaluation of the convergence of the CCM results
To spread the application of CCM to large-scale hydrometeorological research (mentioned in the section 1), this study aims to improve the identification of the convergence value.
The flow chart for evaluating the convergence of the CCM results in this study is shown in figure 2. We firstly calculate the CCM results of SPI-SRI and SPEI-SRI, and then, explore the applicability of the two methods (coefficient of determination R 2 and the coefficient of variation Cv) for evaluating the convergence value.The specific process of these two methods is provide in the supplementary data file.Finally, the convergence value (ρ, used to evaluate the strength of convergence) is calculated.In this study, based on the total number of grids (i.e.19 236) and simple random sampling, we set a random sampling sequence (1, 2, 3, …, 19 236), and then, randomly extract two points from the CCM results of SPI-SRI and two points from the CCM results of SPEI-SRI as representatives for analysis, respectively.

Temporal and spatial variation characteristics of precipitation, runoff, and ET
To better analyze the relationships between different types of droughts, we first analyzed the temporal variability of hydrometeorological factors closely related to meteorological drought and hydrological drought (i.e.precipitation, runoff, and ET).As shown in figures 3(a) and (b), annual precipitation in most areas of China showed an increasing trend, while precipitation in Southwest and Central China showed a decreasing trend.During 1961-2018, the annual precipitation variation range was −18.25-19.01mm/a, and the annual precipitation variation trends were not significant in most regions.The areas with significant changes were mainly in Northwest China, Southwest China, part of the Qinghai-Tibet Plateau, and a few areas in the eastern coastal areas.Annual precipitation in Northwest China, the Qinghai-Tibet Plateau, and a small part of eastern coastal areas showed a significant increasing trend, while annual precipitation in Southwest China showed a significant decreasing trend.In some previous studies, Wang and Zhao (2022) showed that the Northwest region was characterized by warming and humidifying, and Zhang and Zhou (2021) showed that the regional precipitation of the Qinghai-Tibet Plateau showed an increasing trend.These findings are consistent with the results of this study.
In general, the spatial-temporal variation characteristics of runoff and ET are similar to those of annual precipitation.Please refer to the supplementary data file for details.

Convergence of the CCM results
The CCM results can be divided into three categories: unidirectional causality, bidirectional causality, and no causality.In the field of hydrometeorology, meteorological drought is the primary driver of hydrological drought, and there is a clear causal relationship between them.Therefore, this study only considers unidirectional causality and no causality between SPI (SPEI) and SRI.We randomly extract points 16 404 and 2041 from the CCM results of SPI-SRI (as shown in figures 4(a) and (b) and points 12 764 and 6707 from the CCM results of SPEI-SRI (as shown in figures 4(c) and (d) to examine the applicability of the improved causality analysis method.According to the initially hypothesized causality, the CCM result of SPI-SRI converges to about 0.47, and the CCM result of SPEI-SRI converges to about 0.16 (as shown in figures 4(a) and (c)).Therefore, SPEI or SPI has a unidirectional causality to SRI.The results in figures 4(b) and (d) do not show obvious convergence, which means that there is no causality between the corresponding grid SPI (SPEI) and SRI.
However, the method to judge the convergence based on the scatterplot of the CCM results still has limitations.In large-scale hydrometeorological research (e.g. the grid data), it is hard to judge the convergence value one by one through the scatterplot of the CCM results of each grid.Therefore, it is essential to improve the identification of the convergence value.We take figures 4(a) and (c) as examples to explore the applicability of the two methods for evaluating the convergence value, and the results were shown in table 1.
For the first method, the logarithmic function had the best fitting result (figure 4(a) and table 1), while the linear and polynomial fitting results were not ideal.The CCM results gradually converged with the increase in the number of time series length (L), but when ρ was relatively discrete with small L, the results of logarithmic fitting were not good (as shown in figure 4(c)).Therefore, using mathematical equations to evaluate the convergence of the CCM results seems not an appropriate method.
In contrast, Cv was also used to evaluate the convergence of the CCM results.The Cv value in figure 4(a) was 0.028 and that in figure 4(c) was 0.085, both of which could meet the conditions of convergence.The convergence values ρ were 0.4627 and 0.1622 (p < 0.05), respectively, which were consistent with the convergence values in figures 4(a) and (c).The Cv value in figure 4(b) was 0.537 and that in figure 4(d) was 0.162, both of which could not meet the conditions of convergence.Therefore, using Cv to evaluate the convergence of the CCM results can be regarded as an appropriate method.

Correlation and causality between meteorological drought and hydrological drought
Based on the improved CCM in the previous subsection, the causality between meteorological drought and hydrological drought in China was analyzed, and   then, compared with the results from correlation analysis (see figures 5 and 6).
As shown in figures 5(a) and (b), 97.31% of the grids have significant correlation, and 96.88% of the grids have causality.The correlation between SPI and SRI was larger in sub-regions III, IV, V, VI, and VI, but smaller in sub-regions I, II, and VII.
Sub-regions III (eastern part), IV, V, and VI are mainly in Southeast China.Due to the abundant precipitation in these sub-regions, runoff is generally sensitive to precipitation changes (Zhang et al 2011(Zhang et al , 2021)).Sub-region III (western part) is mainly located in Northwest China (mainly the Tarim River Basin), and its runoff is mainly affected by precipitation, followed by glacial meltwater, so the occurrence of hydrological drought mainly depends on the occurrence of meteorological drought (Tang et al 2019).Moreover, the variation trend of precipitation and runoff in Northwest China is significant.Therefore, both correlation and causality were larger in Northwest China.Sub-regions I, II and VII are mainly in Northeast and Southwest China.The correlation was relatively small, especially in the Qinghai-Tibet Plateau.Runoff over the Qinghai-Tibet Plateau and Northeast China was mainly provided by snowmelt, and winter precipitation has little effect on runoff.For example, in the Tibetan Plateau, temperature and solar radiation were both important factors that might influence hydrology through regulating ET (Wu et al 2021, Zhou et al 2021).The southern part of the Qinghai-Tibet Plateau was affected by the external factors of the Indian Ocean southwest monsoon, and the correlation results were relatively poor.The northern part of the Qinghai-Tibet Plateau is mainly located in the Kunlun Mountains, with an average elevation of 5500-6000 m.It is one of the largest glacial regions in China with little precipitation.Therefore, the correlation and causality between precipitation and runoff were relatively poor in the Qinghai-Tibet Plateau.However, in sub-regions I, II, and VII, causality was relatively larger than correlation, especially in the  central and northeastern parts of the Qinghai-Tibet Plateau.There is snowmelt runoff in these areas.Most snowmelt occur in the following spring, which delays hydrological drought.As correlation analysis is based on linear assumptions, snowmelt runoff may affect the correlation between meteorological drought and hydrological drought.On the contrary, CCM is a nonlinear method to identify the causal relationship between the two variables.Since snowmelt may only delay hydrological drought and does not change the unidirectional causality from meteorological drought to hydrological drought, the effect would be relatively smaller in terms of causality.
Precipitation was evenly distributed within the year in Southwest China, and the variation trends of runoff and ET were large.The climate and terrain are complex (Liu et al 2016b, Feng et al 2017, Mokhtar et al 2020, Wang et al 2020).Complex climate characteristics can alter precipitation patterns, while complex terrain can affect the characteristics of runoff yield and concentration, which may affect the relationship between meteorological drought and hydrological drought.Therefore, the correlation and causality between meteorological drought and hydrological drought was relatively smaller in corresponding sub-regions.
As shown in figures 6(a) and (b), 97.63% of the grids have significant correlation, and 96.71% of the grids have causality.The correlation was larger in subregions IV, V, and VI, but smaller in sub-regions I, II, and VII.Similar to the correlation between SPI and SRI, the correlation between SPEI and SRI was relatively smaller in sub-regions I and VII (mainly in the Qinghai-Tibet Plateau and Northeast China).The spatial distribution characteristics of the correlation and causality between SPEI and SRI were similar (see figures 6(a) and (b)), and both larger in the southeast region.However, in Northeast China and the central part of the Qinghai-Tibet Plateau, the causality of some regions showed relatively large characteristics.Similar to the relationship between SPI and SRI, snowmelt runoff may affect the result of correlation, but the effect was relatively smaller in terms of causality.Therefore, in the areas with snowmelt runoff and poor correlation, causality may can better explain the relationship between meteorological drought and hydrological drought.However, the correlation and causal effects of snowmelt on meteorological drought and hydrological drought still need to be further explored.

The application of CCM in this study
The study of causality analysis methods is growing rapidly and is applied to a wide range of fields, such as economics, neuroscience, and epidemiology.However, the application of causality analysis methods in hydrometeorological research is still in its infancy, and a great deal of research is needed to make it mainstream.
In general, CCM can check the bidirectional causality when checking the causality between two variables.In this study, we also get the CCM results of meteorological drought as the cause and hydrological drought as the result in the calculation process.Since there is a clear physical basis that the impact of meteorological drought on hydrological drought is unidirectional, this study does not consider the CCM results of hydrological drought as the cause and meteorological drought as the result.However, in the field of hydrometeorology, the causality between variables is not always clear, such as the relationship between groundwater recharge and runoff, the relationship between vegetation and soil moisture, and so on.When applying the improved CCM in this study, it is necessary to calculate the bidirectional convergence value of the CCM results.In addition to taking Cv as the convergence test, it is also necessary to compare the size of the convergence value.If the direction of the causal relationship is X to Y, then the convergence value of the X to Y cross mapping (ρx) should be greater than Y to X (ρy), especially when ρy converges to a value that is very small or even close to zero.However, when the convergence values are similar, the causal relationship between X and Y is bidirectional.
In our case, we calculated the causality between SPI1, SPEI1 and SRI1, and found that the convergence values in some areas were particularly small.We also find that the correlation between SPI and SRI was negative in sub-regions II and VII, which may be due to the winter precipitation has little influence on runoff, but spring snowmelt will affect the relationship between precipitation and runoff.However, there is still a need for in-depth investigation to elucidate the correlation and causal influence of snowmelt on meteorological and hydrological droughts.The correlation between SPEI and SRI also had negative value in sub-region III (eastern part), which may be due to the impacts of East Asian monsoon on precipitation and evaporation, affecting the relationship between SPEI and SRI (Sun et al 2009).Although causality analysis can detect the causality between variables, it cannot determine the positive or negative influence.Therefore, it was essential to combine the advantage of CCM and PCC to explore the relationship between meteorological drought and hydrological drought.In addition, the spatial distribution characteristics of correlation and causality between SPEI and SRI were very similar to those between SPI and SRI, but in general, the magnitude of causality between SPEI and SRI after considering ET was larger than that between SPI and SRI.After considering ET, the causality of meteorological drought and hydrological drought is more obvious in different climate zones.Therefore, SPEI is more suitable to express the relationship between meteorological drought and hydrological drought.

Extension and limitation
In this study, the meteorological drought index SPI and SPEI were calculated using CN05.1 data, and many studies have demonstrated the reliability of this dataset in drought monitoring in China (Liu et al 2022, Wang et al 2023, Zhang et al 2023).In particular, Yao et al (2018) used meteorological station data combined with historical drought events to verify the applicability of SPI and SPEI in drought monitoring in China.Miao and Gou (2022a) constructed CNRD runoff data using the VIC model.Although there is currently no study on hydrological drought, runoff data has been widely used (Gou et al 2022, Miao et al 2022b), so we consider that it can also well describe the characteristics of hydrological drought in China.Drought index is the most important method in drought assessment at present.However, some studies have pointed out the limitations of relying on index-based methods for drought assessment (Svoboda et al 2015, Rahmati et al 2020, Laimighofer and Laaha 2022).Especially, Laimighofer and Laaha (2022) showed that the uncertainty of standardized drought indices is substantial.Despite these possible limitations, the adaptation of a simplified method by drought indices has facilitated drought characterization for various users and entities (Zargar et al 2011).Therefore, drought index still plays an important role in drought assessment.
The research method proposed in this study enables CCM to be applied in large-scale hydrometeorological studies.However, when using mathematical models to evaluate convergence, the results of convergence rely on predefined mathematical forms of nonlinear functions (such as polynomials and logarithmic functions), which is also a limitation of mathematical model methods.Therefore, it is more appropriate to evaluate the convergence by Cv.In the actual hydrological cycle, meteorological drought took a period of time to trigger hydrological drought, which may reduce the causality relationship.Ye et al (2015) pointed out that CCM with a certain time delay can effectively distinguish the real causality.Wang et al (2018) explored the causality between precipitation and soil moisture by using CCM with time delay.Therefore, CCM with time delay can be used in the future to evaluate the drought propagation.Current studies on drought propagation can be divided into drought propagation probability and drought propagation threshold (such as drought propagation time, duration, and severity).Drought propagation probability model is generally constructed by copula function (Zhu et al 2021, Sadeghfam et al 2022, Bai et al 2023).Drought propagation thresholds, such as duration and severity, are mainly determined by constructing nonlinear equations for different types of drought characteristics (Wu et al 2017, Han et al 2021, Zhou et al 2021b).However, CCM is more likely to be applied to the determination of drought propagation time.In our previous study, by setting different time delays, the time delay when the causality between different types of droughts is the strongest is taken as the drought propagation time (Shi et al 2022a).
In addition, with the continuous development and wide application of artificial intelligence (AI) technology, machine learning has also been applied in drought assessment and propagation.Deo and Sahin (2015) used the extreme learning machine algorithm to assess and predict drought in eastern Australia.Li et al (2023) used independent gridded datasets based on machine learning-assisted upscaling of satellite and in situ observations compared drought propagation in arid and humid regions.Jiang et al (2023) coupling the machine learning model and C-vine copula studied the drought propagation probability from meteorological drought to ecological drought.However, the essence of such machine learning model is a 'black box model' , that is, the model itself has no physical meaning, and its internal operation and decision-making process are not transparent.As a result, pure machine learning models are often criticized by the hydrometeorologists as computer tools that fail to advance human cognition of hydrometeorological processes, which has greatly limited their acceptance by the hydrometeorologists.In recent years, explainable AI (XAI) models have attracted increasing attention in order to use AI to advance human understanding of hydrometeorological processes (Chakraborty et al 2021a, Basagaoglu et al 2022).XAI mainly uses various interpretation techniques to try to analyze the internal decision-making process of AI, so that humans can stand in the perspective of AI to analyze hydrometeorological events.Chakraborty et al (2021b) showed that XAI models have the same good predictive ability as noninterpretable AI models in predicting the watershed-scale reference crop ET.Stef et al (2023) analyzed the impact of institutional quality on CO 2 emissions using XAI.Hu et al (2023) showed that interpretable machine learning is capable of revealing the relationship between climate and crops than 'black box machine learning' .Compared to noninterpretable AI models (e.g.deep learning model), XAI has the capability to unveil interrelations and interdependencies among variables.XAI provides new insights into drought propagation.In future drought propagation studies, the use of XAI models can provide an AI perspective to understand the causal relationship between meteorological and hydrological droughts by identifying key hydrometeorological variables and their thresholds, and can also help develop testable hypotheses to determine drought propagation thresholds.XAI models can offer additional insights into the causal relationship between meteorological and hydrological droughts by accommodating delays in drought propagation, and also unveiling not only the direction but also the nature of the relationships between the variables, whether positive or negative.

Conclusions
In this study, we analyzed the spatial-temporal variation characteristics of precipitation, ET, and runoff, as well as the causality between meteorological drought and hydrological drought in different climatic sub-regions in China.We improved CCM by proposing a method to identify the convergence value, applied the improved CCM to the research based on large-scale grid data, and revealed the applicability of causality analysis in the hydrometeorological field by comparing with the correlation results.The main conclusions are summarized as follows: (1) The spatial-temporal variation characteristics of runoff, ET, and annual precipitation were similar.The annual precipitation, runoff, and ET showed an increasing trend in most areas of China, while a decreasing trend in the southwestern and central parts of China.
(2) The spatial distribution characteristics of correlation and causality between meteorological drought and hydrological drought were similar.
In Southeast China, the correlation and causality were relatively larger; in Northeast China and the central Qinghai-Tibet Plateau, the correlation between meteorological drought and hydrological drought was relatively smaller, but the causality was relatively larger.(3) In view of the spurious correlation, introducing causality analysis can better explain the relationship between meteorological drought and hydrological drought, especially in areas with snowmelt runoff.However, causality analysis cannot explain the positive or negative relationship between variables, so the advantages of the two methods should be given full play when analyzing the relationship between variables.
The application of causality analysis in the field of hydrometeorology is still in its initial stage, and a lot of practice is still needed.This study provides a new perspective for the analysis of the relationship between meteorological drought and hydrological drought.The results are helpful to understand the relationship between meteorological drought and hydrological drought, and can provide reference for drought early warning.Meanwhile, the improvement of convergence identification of CCM in this study lays a foundation for the application of causality analysis in the research of hydrometeorology based on large-scale grid data.

Figure 1 .
Figure 1.The climatic sub-region division of China.

Figure 2 .
Figure 2. Flow chart for evaluating the convergence of the CCM results.

Figure 4 .
Figure 4.The CCM results of SPI-SRI for randomly selected points (a) unidirectional causality (b) no causality and SPEI-SRI for randomly selected points (c) unidirectional causality (d) no causality.

Figure 5 .
Figure 5. Spatial distribution of the PCC (a) and ρ (b) between SPI and SRI; and the box plot of the PCC (c) and ρ (d) in each sub-region.

Figure 6 .
Figure 6.Spatial distribution of the PCC (a) and ρ (b) between SPEI and SRI; and the box plot of the PCC (c) and ρ (d) in each sub-region.

Table 1 .
Fitting equations and Cv.
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